(b) How many hours should be assigned to each graphic designer? 38.4 57.6 Lisa's Hours David's Hours Sarah's Hours 24 What is the total cost (in dollars)? $ 3024 ✔hours ✓hours hours (c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain. Therefore, additional hours for The shadow price for this constraint is 50 x , since the constraint is not binding Lisa will not change the solution.
(b) How many hours should be assigned to each graphic designer? 38.4 57.6 Lisa's Hours David's Hours Sarah's Hours 24 What is the total cost (in dollars)? $ 3024 ✔hours ✓hours hours (c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain. Therefore, additional hours for The shadow price for this constraint is 50 x , since the constraint is not binding Lisa will not change the solution.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
![Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that
120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior
designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View
Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To
provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number:
of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project
commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18
for Sarah.
(a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project
to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is
assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Min 30L + 25D + 185
S.L.
Minimum Lisa
Minimum Sarah
Maximum Lisa
Maximum Sarah
Taral Time
L≥0.4(D+L)
$20.15(L+D+S)
L≤ 50
S≤ 25 (D+ L)
I+D+S 120](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d8fb038-8950-47bc-91e9-50d922788bb9%2Fde4e1078-b2f2-45af-8bbb-d3d1d46c1c10%2F3572pbe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that
120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior
designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View
Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To
provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number:
of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project
commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18
for Sarah.
(a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project
to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is
assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Min 30L + 25D + 185
S.L.
Minimum Lisa
Minimum Sarah
Maximum Lisa
Maximum Sarah
Taral Time
L≥0.4(D+L)
$20.15(L+D+S)
L≤ 50
S≤ 25 (D+ L)
I+D+S 120
![(b) How many hours should be assigned to each graphic designer?
Lisa's Hours
38.4
David's Hours
57.6
Sarah's Hours
24
What is the total cost (in dollars)?
$ 3024
✓hours
✓hours
hours
(c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain.
The shadow price for this constraint is 50
Lisa will not
change the solution.
X, since the constraint is not binding ✔ Therefore, additional hours for
(d) If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain.
The shadow price for this constraint is
, since the constraint is not binding
.Therefore, assigning fewer hours to
Sarah will not
change the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d8fb038-8950-47bc-91e9-50d922788bb9%2Fde4e1078-b2f2-45af-8bbb-d3d1d46c1c10%2Ftoh9szg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) How many hours should be assigned to each graphic designer?
Lisa's Hours
38.4
David's Hours
57.6
Sarah's Hours
24
What is the total cost (in dollars)?
$ 3024
✓hours
✓hours
hours
(c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain.
The shadow price for this constraint is 50
Lisa will not
change the solution.
X, since the constraint is not binding ✔ Therefore, additional hours for
(d) If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain.
The shadow price for this constraint is
, since the constraint is not binding
.Therefore, assigning fewer hours to
Sarah will not
change the solution.
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